PreprintCC BY 4.0arXiv
Crepant resolutions of four-dimensional finite quotients
Abstract
We give counterexamples to the conjecture of Dais-Henk-Ziegler on projective crepant resolutions of complete-intersection quotient singularities. For finite G⊂SL4(ℤ), we determine whether ℂ4/G admits a projective crepant resolution, with the representations considered up to conjugacy in SL4(ℂ). Ten explicit criteria decide all cases. The examples also show that the Molien series and the age polynomial do not determine existence. We also discuss questions of Ito-Reid on maximal cyclic subgroups and the generation of cohomology in degree two.
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BibTeX
@misc{burek2026crepant,
title = {{Crepant resolutions of four-dimensional finite quotients}},
author = {Dominik Burek and Sławomir Cynk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16962},
eprint = {2610.16962},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16962},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Crepant resolutions of four-dimensional finite quotients
AU - Dominik Burek
AU - Sławomir Cynk
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16962
UR - https://arxiv.org/abs/2610.16962
AB - We give counterexamples to the conjecture of Dais-Henk-Ziegler on projective crepant resolutions of complete-intersection quotient singularities. For finite G⊂SL_4(ℤ), we determine whether ℂ^4/G admits a projective crepant resolution, with the representations considered up to conjugacy in SL_4(ℂ). Ten explicit criteria decide all cases. The examples also show that the Molien series and the age polynomial do not determine existence. We also discuss questions of Ito-Reid on maximal cyclic subgroups and the generation of cohomology in degree two.
ER -